No. As a seasoned tereré drinker, the fact that you're drinking lots of (mostly) cold water, added to the higher polar and ionic charge of various organic compounds and soluble mineral found in it, should somewhat encourage movement of your lower intestinal tract. Doctors here do not discourage drinking of tereré, but warn that it does not hydrate the body properly, but the contrary. And this is one of the reasons: in the balance, your body loses more water than it gains, so you should supplement it with regular hydration.

There's also the fact that regular Camellia sinensis tea has astringent properties, and people keep expecting that yerba mate, being a "herbal tea", might have similar effects, when in fact it doesn't.

Of course, as parent stated, many people never experience such effects. YMMV.